1+[(1+cos theta-sin^(2)theta)/(sin theta(1+cos theta))]^(2)=(1)/(sin^(2)theta)

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

(sin theta-cos theta)/(sin theta+cos theta)+(sin theta+cos theta)/(sin theta-cos theta)=(2)/((2sin^(2)theta-1))

Prove the following identity: ((1)/(sec^(2)theta-cos^(2)theta)+(1)/(cos ec^(2)theta-sin^(2)theta))sin^(2)theta cos^(2)theta=(1-sin^(2)theta cos^(2)theta)/(2+sin^(2)cos^(2)theta)

(sin^(2) theta)/(1-cos theta)-(cos^(2) theta)/(1-sin theta)=cos theta-sin theta

1-(sin^(2) theta)/(1+cos theta) + (1+cos theta)/(sin theta) - (sin theta)/(1-cos theta) - (1)/(sec theta)=

1- (sin ^ (2) theta) / (1 + cos theta) + (1 + cos theta) / (sin theta) - (sin theta) / (1-cos theta) - (1) / (sec theta)

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))